Tom,
Why the reluctance?
Mike:
It's not so much a reluctance, as I just don't see them so easily.
I tend to route a course by looking for sight lines -- on paper, as well as when I'm out walking the site. In either case, it doesn't normally occur to me to go "up and over" that hill, when I can't see what the result will be, if there is another obvious green site beckoning in the distance, clearly visible. I have to train myself to look for that; it's not natural to me. I'm always surprised that Bill Coore usually includes one or two in his routings, because he finds them on foot, and they never seem obvious on foot!
I probably would never have come up with the 3rd at Stonewall if that hill hadn't been such an awkward distance from the road and from another drop off. Not going over the hill would have limited that nine holes to a bunch of 300- or 350-yard holes playing up and down its slope. [Luckily, I thought of the 4th at Royal Melbourne at the right moment.] Indeed, it's the same for the Old Course ... with a tight acreage and Route 345 only 250-300 yards from the top of the hill, Tom Fazio didn't have any choice but to have some up and over holes if he wanted to use that end of the property, and he needed it to get 18 holes.
I have built more of these holes than I realized in my initial post. The 17th at Dismal River (Red) is one of my favorites. The sixth at Medinah #1. The 9th at Streamsong, as Kyle mentioned; also the 6th and the 18th. The 3rd and 4th at Old Macdonald. The sixth at Sebonack. The 16th at Ballyneal. The 13th at St. Andrews Beach, which Aussies are still complaining about! The 4th at Cape Kidnappers. And the 9th at Pacific Dunes, if you play to the lower green.
There are many more up and over holes that are classics, if you don't have to have the fallaway green as part of the package. The one I'm surprised no one has mentioned is the 8th at Pebble Beach.